The L^∞ norm, also known as the infinity norm or maximum norm, is a way to measure the size of a vector in a mathematical space. It is defined as the maximum absolute value of the components of the vector. For example, for a vector v = (v₁, v₂, ..., vₙ), the L^∞ norm is calculated as ||v||₊ = max(|v₁|, |v₂|, ..., |vₙ|). This norm is particularly useful in various fields, including functional analysis and optimization, as it provides a straightforward way to assess the largest deviation among the vector's elements. It helps in comparing different vectors and is often used in algorithms that require bounding or limiting values.